Let us note moreover that some quality functions allow optimizations concerning the computation of the \(q(\mathcal {C})\) : for example it is possible to compute efficiently \(q(\mathcal {C}_1 \cup \mathcal {C}_2)\)  from the values of \(q(\mathcal {C}_1)\)  and \(q(\mathcal {C}_2)\)  for the modularity [1]} and for random walk quality function [2]}, [3]}.
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